emily is constructing a triangle one side is 3 inches long and another is 5 inches long which of the following is the smallest measure emily could use for the third side of the triangle

To find the smallest possible measure for the third side of the triangle, you can apply the triangle inequality theorem. According to this theorem, for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.

In this case, let's denote the length of the third side as "x". So, according to the theorem, we have two inequalities:

1. 3 + 5 > x (the sum of the first two sides must be greater than the third side)
2. 3 + x > 5 (the sum of the first and third sides must be greater than the second side)

Now, we can simplify these inequalities to find the smallest measure for the third side:

1. 8 > x
2. 3 > x - 5
8 > x

From these inequalities, we can conclude that the maximum value for "x" is 8. However, in order to find the smallest possible measure for the third side, we need to find the minimum value for "x".

Since x cannot be negative (as we are dealing with lengths), the smallest measure for the third side would be 0 (zero) inches. Note that a triangle with a third side of length 0 would not be a valid triangle.

no choices shown, but any number x such that 2 < x < 8 will work.

Why those values? Any side of a triangle must be less than the sum of the other two sides. Otherwise they will not reach, even if laid out end-to-end. So,

x < 5+3
5 < 3+x
3 < 5+x